10. TWO-DIMENSIONAL UNITARY TRANSFORMATIONS

There are three main areas of application of two-dimensional unitary transformations for image processing. First, the transformations are used to highlight the characteristic features of the image. For example, the constant component of the Fourier spectrum is proportional to the average brightness of the image, and the high-frequency components characterize the size and orientation of its contours. Another area of ​​application for transformations is image coding, when the spectrum width is reduced by discarding or coarse quantization of small transform coefficients. The third application area is the reduction in dimension when performing calculations. In other words, in the course of processing (for example, filtering) small conversion factors can be discarded without a noticeable deterioration in the quality of processing. In subsequent chapters, these applications will be described in more detail. This chapter discusses the properties of the transformations most commonly encountered in image processing.